If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m?
A) m+6
B) m+7*****
C) 2m+14
D) 3m+21
x = (m+9)/2
y = (2m+15)/2
z = (3m+18)/2
we want (x+y+z)/3
x+y+z = (1/2) (6m+42)
(x+y+z)/3 = (1/6)(6m+42)
= m + 7
so we agree
no
To find the average of x, y, and z in terms of m, we need to add all their values and divide by the total number of values.
x = (m + 9)
y = (2m + 15)
z = (3m + 18)
To find the average (arithmetic mean), we add the values of x, y, and z and then divide by 3 (the total number of values).
Average = (x + y + z) / 3
Substitute the values of x, y, and z into the equation:
Average = ((m + 9) + (2m + 15) + (3m + 18)) / 3
= (m + 2m + 3m + 9 + 15 + 18) / 3
= (6m + 42) / 3
= 2m + 14
Therefore, the average of x, y, and z in terms of m is 2m + 14.
Hence, the correct option is C) 2m + 14.
To find the average of x, y, and z in terms of m, we need to first find the expressions for x, y, and z in terms of m, and then take their average.
We are given that x is the average of m and 9. The average of two numbers is obtained by summing the numbers and dividing by 2. So, x = (m + 9) / 2.
Similarly, y is the average of 2m and 15. Therefore, y = (2m + 15) / 2.
Lastly, z is the average of 3m and 18. Thus, z = (3m + 18) / 2.
To find the average of x, y, and z, we add them all together and divide by 3 (since we have three numbers). So, average = (x + y + z) / 3.
Substituting the expressions for x, y, and z, we have average = ((m + 9) / 2 + (2m + 15) / 2 + (3m + 18) / 2) / 3.
Now, we simplify the expression by combining like terms:
average = (m + 9 + 2m + 15 + 3m + 18) / 2 / 3
= (6m + 42) / 2 / 3
= (6m + 42) / 6
= 6m / 6 + 42 / 6
= m + 7.
Therefore, the average of x, y, and z in terms of m is m + 7.
Hence, the correct answer is B) m + 7.